This paper proposes a novel signed $\beta$-model for directed signed network, which is frequently encountered in application domains but largely neglected in literature. The proposed signed $\beta$-model decomposes a directed signed network as the difference of two unsigned networks and embeds each node with two latent factors for in-status and out-status. The presence of negative edges leads to a non-concave log-likelihood, and a one-step estimation algorithm is developed to facilitate parameter estimation, which is efficient both theoretically and computationally. We also develop an inferential procedure for pairwise and multiple node comparisons under the signed $\beta$-model, which fills the void of lacking uncertainty quantification for node ranking. Theoretical results are established for the coverage probability of confidence interval, as well as the false discovery rate (FDR) control for multiple node comparison. The finite sample performance of the signed $\beta$-model is also examined through extensive numerical experiments on both synthetic and real-life networks.
翻译:本文建议为直接签署网络建立一个经过签名的$\beta$模型,该模型在应用领域经常遇到,但在文献中大都被忽视。所签名的$\beta$模型将一个直接签名的网络分解成两个未签名网络的差异,每个节点嵌入状态和超状态的两个潜在因素。负边缘的存在导致非加密日志相似性,并开发了一个一步骤的估计算法,以便于在理论上和计算上都高效的参数估计。我们还开发了一个在经过签名的$\beta$模型下进行对比和多节点比较的推断程序,以填补节点排序缺乏不确定性量化的空白。为信任期的覆盖概率以及多节点比较的虚假发现率控制确定了理论结果。还通过对合成网络和现实生命网络进行广泛的数字实验,对所签名的美元模型的有限样本性能进行了审查。